LMFDB - Embedded newform 392.3.k.n.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 $ x^16 - x^15 + 3x^14 + 6x^13 - 22x^12 + 44x^11 - 20x^10 - 112x^9 + 368x^8 - 448x^7 - 320x^6 + 2816x^5 - 5632x^4 + 6144x^3 + 12288x^2 - 16384x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.1
Root			$-0.575587 - 1.91538i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.n.67.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94657 + 0.459219i) q^{2} +(-2.61182 - 4.52380i) q^{3} +(3.57824 - 1.78780i) q^{4} +(5.42814 + 3.13394i) q^{5} +(7.16148 + 7.60647i) q^{6} +(-6.14428 + 5.12327i) q^{8} +(-9.14316 + 15.8364i) q^{9} +O(q^{10})$	\(q+(-1.94657 + 0.459219i) q^{2} +(-2.61182 - 4.52380i) q^{3} +(3.57824 - 1.78780i) q^{4} +(5.42814 + 3.13394i) q^{5} +(7.16148 + 7.60647i) q^{6} +(-6.14428 + 5.12327i) q^{8} +(-9.14316 + 15.8364i) q^{9} +(-12.0054 - 3.60771i) q^{10} +(-4.90344 - 8.49301i) q^{11} +(-17.4333 - 11.5178i) q^{12} -2.41653i q^{13} -32.7411i q^{15} +(9.60754 - 12.7943i) q^{16} +(3.44726 + 5.97083i) q^{17} +(10.5254 - 35.0253i) q^{18} +(1.38818 - 2.40441i) q^{19} +(25.0260 + 1.50954i) q^{20} +(13.4450 + 14.2804i) q^{22} +(-37.0947 - 21.4166i) q^{23} +(39.2243 + 14.4144i) q^{24} +(7.14316 + 12.3723i) q^{25} +(1.10972 + 4.70393i) q^{26} +48.5083 q^{27} -37.3505i q^{29} +(15.0353 + 63.7327i) q^{30} +(6.20797 - 3.58417i) q^{31} +(-12.8263 + 29.3170i) q^{32} +(-25.6138 + 44.3643i) q^{33} +(-9.45224 - 10.0396i) q^{34} +(-4.40402 + 73.0126i) q^{36} +(0.175502 + 0.101326i) q^{37} +(-1.59804 + 5.31782i) q^{38} +(-10.9319 + 6.31153i) q^{39} +(-49.4080 + 8.55402i) q^{40} -63.5494 q^{41} -35.3384 q^{43} +(-32.7295 - 21.6236i) q^{44} +(-99.2607 + 57.3082i) q^{45} +(82.0421 + 24.6543i) q^{46} +(-32.8335 - 18.9564i) q^{47} +(-82.9721 - 10.0461i) q^{48} +(-19.5862 - 20.8032i) q^{50} +(18.0072 - 31.1894i) q^{51} +(-4.32027 - 8.64691i) q^{52} +(-47.3414 + 27.3326i) q^{53} +(-94.4246 + 22.2759i) q^{54} -61.4684i q^{55} -14.5027 q^{57} +(17.1521 + 72.7051i) q^{58} +(52.3975 + 90.7551i) q^{59} +(-58.5345 - 117.155i) q^{60} +(37.9032 + 21.8834i) q^{61} +(-10.4383 + 9.82765i) q^{62} +(11.5043 - 62.9575i) q^{64} +(7.57325 - 13.1173i) q^{65} +(29.4859 - 98.1204i) q^{66} +(-15.5510 - 26.9352i) q^{67} +(23.0098 + 15.2020i) q^{68} +223.745i q^{69} +23.1294i q^{71} +(-24.9561 - 144.146i) q^{72} +(-34.6138 - 59.9528i) q^{73} +(-0.388158 - 0.116644i) q^{74} +(37.3132 - 64.6284i) q^{75} +(0.668652 - 11.0853i) q^{76} +(18.3813 - 17.3059i) q^{78} +(-17.2624 - 9.96642i) q^{79} +(92.2478 - 39.3401i) q^{80} +(-44.4063 - 76.9139i) q^{81} +(123.703 - 29.1831i) q^{82} +5.11617 q^{83} +43.2140i q^{85} +(68.7885 - 16.2281i) q^{86} +(-168.966 + 97.5525i) q^{87} +(73.6400 + 27.0618i) q^{88} +(-8.99444 + 15.5788i) q^{89} +(166.901 - 157.137i) q^{90} +(-171.022 - 10.3158i) q^{92} +(-32.4282 - 18.7224i) q^{93} +(72.6178 + 21.8222i) q^{94} +(15.0705 - 8.70097i) q^{95} +(166.124 - 18.5470i) q^{96} -12.4864 q^{97} +179.332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.94657	+	0.459219i	−0.973283	+	0.229610i
$2$	−1.94657	+	0.459219i	−0.973283	+	0.229610i
$3$	−2.61182	−	4.52380i	−0.870605	−	1.50793i	−0.861372	−	0.507975i	$-0.830394\pi$
$3$	−2.61182	−	4.52380i	−0.870605	−	1.50793i	−0.00923321	−	0.999957i	$-0.502939\pi$
$4$	3.57824	−	1.78780i	0.894559	−	0.446950i
$5$	5.42814	+	3.13394i	1.08563	+	0.626788i	0.932409	−	0.361404i	$-0.117703\pi$
$5$	5.42814	+	3.13394i	1.08563	+	0.626788i	0.153219	+	0.988192i	$0.451036\pi$
$6$	7.16148	+	7.60647i	1.19358	+	1.26775i
$7$		0			0
$7$		0			0
$8$	−6.14428	+	5.12327i	−0.768035	+	0.640408i
$9$	−9.14316	+	15.8364i	−1.01591	+	1.75960i
$10$	−12.0054	−	3.60771i	−1.20054	−	0.360771i
$11$	−4.90344	−	8.49301i	−0.445767	−	0.772092i	0.552338	−	0.833620i	$-0.313736\pi$
$11$	−4.90344	−	8.49301i	−0.445767	−	0.772092i	−0.998105	+	0.0615286i	$0.980402\pi$
$12$	−17.4333	−	11.5178i	−1.45278	−	0.959817i
$13$		−	2.41653i		−	0.185887i	−0.995671	−	0.0929434i	$-0.970372\pi$
$13$		−	2.41653i		−	0.185887i	0.995671	−	0.0929434i	$-0.0296276\pi$
$14$		0			0
$15$		−	32.7411i		−	2.18274i
$16$	9.60754	−	12.7943i	0.600471	−	0.799646i
$17$	3.44726	+	5.97083i	0.202780	+	0.351225i	0.949423	−	0.313999i	$-0.101669\pi$
$17$	3.44726	+	5.97083i	0.202780	+	0.351225i	−0.746643	+	0.665225i	$0.768336\pi$
$18$	10.5254	−	35.0253i	0.584743	−	1.94585i
$19$	1.38818	−	2.40441i	0.0730624	−	0.126548i	−0.827180	−	0.561938i	$-0.810056\pi$
$19$	1.38818	−	2.40441i	0.0730624	−	0.126548i	0.900242	+	0.435390i	$0.143389\pi$
$20$	25.0260	+	1.50954i	1.25130	+	0.0754769i
$21$		0			0
$22$	13.4450	+	14.2804i	0.611137	+	0.649111i
$23$	−37.0947	−	21.4166i	−1.61281	−	0.931157i	−0.988715	−	0.149811i	$-0.952134\pi$
$23$	−37.0947	−	21.4166i	−1.61281	−	0.931157i	−0.624097	−	0.781347i	$-0.714533\pi$
$24$	39.2243	+	14.4144i	1.63435	+	0.600602i
$25$	7.14316	+	12.3723i	0.285726	+	0.494893i
$26$	1.10972	+	4.70393i	0.0426814	+	0.180920i
$27$	48.5083			1.79660
$28$		0			0
$29$		−	37.3505i		−	1.28795i	−0.765048	−	0.643974i	$-0.777285\pi$
$29$		−	37.3505i		−	1.28795i	0.765048	−	0.643974i	$-0.222715\pi$
$30$	15.0353	+	63.7327i	0.501178	+	2.12442i
$31$	6.20797	−	3.58417i	0.200257	−	0.115619i	−0.396518	−	0.918027i	$-0.629782\pi$
$31$	6.20797	−	3.58417i	0.200257	−	0.115619i	0.596775	+	0.802408i	$0.296448\pi$
$32$	−12.8263	+	29.3170i	−0.400822	+	0.916156i
$33$	−25.6138	+	44.3643i	−0.776175	+	1.34437i
$34$	−9.45224	−	10.0396i	−0.278007	−	0.295281i
$35$		0			0
$36$	−4.40402	+	73.0126i	−0.122334	+	2.02813i
$37$	0.175502	+	0.101326i	0.00474330	+	0.00273855i	0.502370	−	0.864653i	$-0.332462\pi$
$37$	0.175502	+	0.101326i	0.00474330	+	0.00273855i	−0.497626	+	0.867391i	$0.665795\pi$
$38$	−1.59804	+	5.31782i	−0.0420538	+	0.139943i
$39$	−10.9319	+	6.31153i	−0.280305	+	0.161834i
$40$	−49.4080	+	8.55402i	−1.23520	+	0.213851i
$41$	−63.5494			−1.54999			−0.774993	−	0.631970i	$-0.782247\pi$
$41$	−63.5494			−1.54999			−0.774993	+	0.631970i	$0.782247\pi$
$42$		0			0
$43$	−35.3384			−0.821823			−0.410911	−	0.911675i	$-0.634789\pi$
$43$	−35.3384			−0.821823			−0.410911	+	0.911675i	$0.634789\pi$
$44$	−32.7295	−	21.6236i	−0.743852	−	0.491446i
$45$	−99.2607	+	57.3082i	−2.20579	+	1.27352i
$46$	82.0421	+	24.6543i	1.78352	+	0.535962i
$47$	−32.8335	−	18.9564i	−0.698586	−	0.403329i	0.108235	−	0.994125i	$-0.465480\pi$
$47$	−32.8335	−	18.9564i	−0.698586	−	0.403329i	−0.806820	+	0.590797i	$0.798814\pi$
$48$	−82.9721	−	10.0461i	−1.72859	−	0.209294i
$49$		0			0
$50$	−19.5862	−	20.8032i	−0.391725	−	0.416065i
$51$	18.0072	−	31.1894i	0.353083	−	0.611557i
$52$	−4.32027	−	8.64691i	−0.0830821	−	0.166287i
$53$	−47.3414	+	27.3326i	−0.893234	+	0.515709i	−0.874999	−	0.484125i	$-0.839138\pi$
$53$	−47.3414	+	27.3326i	−0.893234	+	0.515709i	−0.0182349	+	0.999834i	$0.505805\pi$
$54$	−94.4246	+	22.2759i	−1.74860	+	0.412517i
$55$		−	61.4684i		−	1.11761i
$56$		0			0
$57$	−14.5027			−0.254434
$58$	17.1521	+	72.7051i	0.295725	+	1.25354i
$59$	52.3975	+	90.7551i	0.888093	+	1.53822i	0.842128	+	0.539278i	$0.181303\pi$
$59$	52.3975	+	90.7551i	0.888093	+	1.53822i	0.0459650	+	0.998943i	$0.485364\pi$
$60$	−58.5345	−	117.155i	−0.975576	−	1.95259i
$61$	37.9032	+	21.8834i	0.621364	+	0.358745i	0.777400	−	0.629007i	$-0.216538\pi$
$61$	37.9032	+	21.8834i	0.621364	+	0.358745i	−0.156036	+	0.987751i	$0.549872\pi$
$62$	−10.4383	+	9.82765i	−0.168360	+	0.158511i
$63$		0			0
$64$	11.5043	−	62.9575i	0.179755	−	0.983711i
$65$	7.57325	−	13.1173i	0.116512	−	0.201804i
$66$	29.4859	−	98.1204i	0.446756	−	1.48667i
$67$	−15.5510	−	26.9352i	−0.232105	−	0.402018i	0.726322	−	0.687354i	$-0.241228\pi$
$67$	−15.5510	−	26.9352i	−0.232105	−	0.402018i	−0.958427	+	0.285336i	$0.907895\pi$
$68$	23.0098	+	15.2020i	0.338379	+	0.223559i
$69$			223.745i			3.24268i
$70$		0			0
$71$			23.1294i			0.325766i	0.986645	+	0.162883i	$0.0520794\pi$
$71$			23.1294i			0.325766i	−0.986645	+	0.162883i	$0.947921\pi$
$72$	−24.9561	−	144.146i	−0.346612	−	2.00203i
$73$	−34.6138	−	59.9528i	−0.474161	−	0.821271i	0.525401	−	0.850855i	$-0.323915\pi$
$73$	−34.6138	−	59.9528i	−0.474161	−	0.821271i	−0.999562	+	0.0295834i	$0.990582\pi$
$74$	−0.388158	−	0.116644i	−0.00524537	−	0.00157627i
$75$	37.3132	−	64.6284i	0.497510	−	0.861712i
$76$	0.668652	−	11.0853i	0.00879806	−	0.145860i
$77$		0			0
$78$	18.3813	−	17.3059i	0.235657	−	0.221871i
$79$	−17.2624	−	9.96642i	−0.218511	−	0.126157i	0.386750	−	0.922185i	$-0.373598\pi$
$79$	−17.2624	−	9.96642i	−0.218511	−	0.126157i	−0.605261	+	0.796027i	$0.706931\pi$
$80$	92.2478	−	39.3401i	1.15310	−	0.491751i
$81$	−44.4063	−	76.9139i	−0.548225	−	0.949554i
$82$	123.703	−	29.1831i	1.50857	−	0.355892i
$83$	5.11617			0.0616406			0.0308203	−	0.999525i	$-0.490188\pi$
$83$	5.11617			0.0616406			0.0308203	+	0.999525i	$0.490188\pi$
$84$		0			0
$85$			43.2140i			0.508400i
$86$	68.7885	−	16.2281i	0.799866	−	0.188698i
$87$	−168.966	+	97.5525i	−1.94214	+	1.12129i
$88$	73.6400	+	27.0618i	0.836819	+	0.307520i
$89$	−8.99444	+	15.5788i	−0.101061	+	0.175043i	−0.912122	−	0.409919i	$-0.865557\pi$
$89$	−8.99444	+	15.5788i	−0.101061	+	0.175043i	0.811061	+	0.584962i	$0.198890\pi$
$90$	166.901	−	157.137i	1.85445	−	1.74596i
$91$		0			0
$92$	−171.022	−	10.3158i	−1.85894	−	0.112129i
$93$	−32.4282	−	18.7224i	−0.348690	−	0.201316i
$94$	72.6178	+	21.8222i	0.772530	+	0.232151i
$95$	15.0705	−	8.70097i	0.158637	−	0.0915892i
$96$	166.124	−	18.5470i	1.73046	−	0.193198i
$97$	−12.4864			−0.128726			−0.0643629	−	0.997927i	$-0.520502\pi$
$97$	−12.4864			−0.128726			−0.0643629	+	0.997927i	$0.520502\pi$
$98$		0			0
$99$	179.332			1.81143
$100$	47.6791	+	31.5005i	0.476791	+	0.315005i
$101$	58.9549	−	34.0376i	0.583712	−	0.337006i	−0.178895	−	0.983868i	$-0.557252\pi$
$101$	58.9549	−	34.0376i	0.583712	−	0.337006i	0.762607	+	0.646862i	$0.223919\pi$
$102$	−20.7295	+	68.9815i	−0.203230	+	0.676289i
$103$	−50.4833	−	29.1465i	−0.490129	−	0.282976i	0.234499	−	0.972116i	$-0.424655\pi$
$103$	−50.4833	−	29.1465i	−0.490129	−	0.282976i	−0.724628	+	0.689140i	$0.757988\pi$
$104$	12.3805	+	14.8478i	0.119043	+	0.142768i
$105$		0			0
$106$	79.6015	−	74.9447i	0.750957	−	0.707026i
$107$	−67.9340	+	117.665i	−0.634897	+	1.09967i	0.351640	+	0.936135i	$0.385624\pi$
$107$	−67.9340	+	117.665i	−0.634897	+	1.09967i	−0.986537	+	0.163538i	$0.947709\pi$
$108$	173.574	−	86.7231i	1.60717	−	0.802992i
$109$	38.5365	−	22.2490i	0.353546	−	0.204120i	−0.312700	−	0.949852i	$-0.601234\pi$
$109$	38.5365	−	22.2490i	0.353546	−	0.204120i	0.666246	+	0.745732i	$0.267900\pi$
$110$	28.2274	+	119.652i	0.256613	+	1.08775i
$111$		−	1.05858i		−	0.00953677i
$112$		0			0
$113$	−133.391			−1.18045			−0.590224	−	0.807240i	$-0.700961\pi$
$113$	−133.391			−1.18045			−0.590224	+	0.807240i	$0.700961\pi$
$114$	28.2305	−	6.65993i	0.247636	−	0.0584204i
$115$	−134.237	−	232.505i	−1.16728	−	2.02178i
$116$	−66.7752	−	133.649i	−0.575648	−	1.15214i
$117$	38.2691	+	22.0947i	0.327087	+	0.188844i
$118$	−143.672	−	152.599i	−1.21756	−	1.29321i
$119$		0			0
$120$	167.741	+	201.170i	1.39784	+	1.67642i
$121$	12.4125	−	21.4991i	0.102583	−	0.177679i
$122$	−83.8304	−	25.1916i	−0.687134	−	0.206489i
$123$	165.979	+	287.485i	1.34943	+	2.33727i
$124$	15.8058	−	23.9236i	0.127466	−	0.192933i
$125$		−	67.1521i		−	0.537217i
$126$		0			0
$127$		−	130.977i		−	1.03131i	−0.856795	−	0.515657i	$-0.827548\pi$
$127$		−	130.977i		−	1.03131i	0.856795	−	0.515657i	$-0.172452\pi$
$128$	6.51744	+	127.834i	0.0509175	+	0.998703i
$129$	92.2973	+	159.864i	0.715483	+	1.23925i
$130$	−8.71814	+	29.0114i	−0.0670626	+	0.223165i
$131$	−26.6655	+	46.1861i	−0.203554	+	0.352565i	−0.949671	−	0.313249i	$-0.898583\pi$
$131$	−26.6655	+	46.1861i	−0.203554	+	0.352565i	0.746117	+	0.665815i	$0.231916\pi$
$132$	−12.3375	+	204.538i	−0.0934658	+	1.54953i
$133$		0			0
$134$	42.6403	+	45.2898i	0.318211	+	0.337983i
$135$	263.310	+	152.022i	1.95044	+	1.12609i
$136$	−51.7711	−	19.0252i	−0.380670	−	0.139891i
$137$	28.8589	+	49.9852i	0.210649	+	0.364855i	0.951918	−	0.306353i	$-0.0991089\pi$
$137$	28.8589	+	49.9852i	0.210649	+	0.364855i	−0.741269	+	0.671208i	$0.765776\pi$
$138$	−102.748	−	435.534i	−0.744551	−	3.15605i
$139$	172.422			1.24045			0.620224	−	0.784425i	$-0.287042\pi$
$139$	172.422			1.24045			0.620224	+	0.784425i	$0.287042\pi$
$140$		0			0
$141$			198.043i			1.40456i
$142$	−10.6215	−	45.0229i	−0.0747991	−	0.317063i
$143$	−20.5236	+	11.8493i	−0.143522	+	0.0828623i
$144$	114.773	+	269.130i	0.797037	+	1.86896i
$145$	117.054	−	202.744i	0.807270	−	1.39823i
$146$	94.9094	+	100.807i	0.650065	+	0.690457i
$147$		0			0
$148$	0.809139	+	0.0488062i	0.00546716	+	0.000329772i
$149$	−190.117	−	109.764i	−1.27596	−	0.736673i	−0.299853	−	0.953985i	$-0.596938\pi$
$149$	−190.117	−	109.764i	−1.27596	−	0.736673i	−0.976102	+	0.217312i	$0.930271\pi$
$150$	−42.9540	+	142.938i	−0.286360	+	0.952922i
$151$	−160.793	+	92.8340i	−1.06486	+	0.614795i	−0.926771	−	0.375626i	$-0.877428\pi$
$151$	−160.793	+	92.8340i	−1.06486	+	0.614795i	−0.138084	+	0.990421i	$0.544094\pi$
$152$	3.78902	+	21.8854i	0.0249278	+	0.143983i
$153$	−126.075			−0.824022
$154$		0			0
$155$	44.9304			0.289873
$156$	−27.8331	+	42.1281i	−0.178417	+	0.270052i
$157$	162.970	−	94.0909i	1.03803	−	0.599305i	0.118753	−	0.992924i	$-0.462110\pi$
$157$	162.970	−	94.0909i	1.03803	−	0.599305i	0.919274	+	0.393619i	$0.128777\pi$
$158$	38.1791	+	11.4731i	0.241640	+	0.0726145i
$159$	247.294	+	142.775i	1.55531	+	0.897957i
$160$	−161.501	+	118.940i	−1.00938	+	0.743375i
$161$		0			0
$162$	121.760	+	129.326i	0.751605	+	0.798307i
$163$	−27.2577	+	47.2117i	−0.167225	+	0.289642i	−0.937443	−	0.348138i	$-0.886814\pi$
$163$	−27.2577	+	47.2117i	−0.167225	+	0.289642i	0.770218	+	0.637781i	$0.220147\pi$
$164$	−227.395	+	113.614i	−1.38655	+	0.692766i
$165$	−278.070	+	160.544i	−1.68527	+	0.972994i
$166$	−9.95897	+	2.34945i	−0.0599938	+	0.0141533i
$167$		−	266.435i		−	1.59542i	−0.603042	−	0.797709i	$-0.706045\pi$
$167$		−	266.435i		−	1.59542i	0.603042	−	0.797709i	$-0.293955\pi$
$168$		0			0
$169$	163.160			0.965446
$170$	−19.8447	−	84.1190i	−0.116734	−	0.494817i
$171$	25.3848	+	43.9677i	0.148449	+	0.257121i
$172$	−126.449	+	63.1780i	−0.735169	+	0.367314i
$173$	99.4501	+	57.4175i	0.574856	+	0.331893i	0.759086	−	0.650990i	$-0.225646\pi$
$173$	99.4501	+	57.4175i	0.574856	+	0.331893i	−0.184231	+	0.982883i	$0.558979\pi$
$174$	284.105	−	267.485i	1.63279	−	1.53727i
$175$		0			0
$176$	−155.772	−	18.8606i	−0.885071	−	0.107162i
$177$	273.705	−	474.071i	1.54636	−	2.67837i
$178$	10.3542	−	34.4556i	0.0581695	−	0.193571i
$179$	−56.4243	−	97.7298i	−0.315220	−	0.545977i	0.664264	−	0.747498i	$-0.268745\pi$
$179$	−56.4243	−	97.7298i	−0.315220	−	0.545977i	−0.979484	+	0.201521i	$0.935412\pi$
$180$	−252.723	+	382.521i	−1.40401	+	2.12512i
$181$		−	60.9470i		−	0.336724i	−0.985725	−	0.168362i	$-0.946152\pi$
$181$		−	60.9470i		−	0.336724i	0.985725	−	0.168362i	$-0.0538477\pi$
$182$		0			0
$183$		−	228.622i		−	1.24930i
$184$	337.643	−	58.4562i	1.83502	−	0.317697i
$185$	0.635101	+	1.10003i	0.00343298	+	0.00594609i
$186$	71.7212	+	21.5528i	0.385598	+	0.115875i
$187$	33.8069	−	58.5552i	0.180785	−	0.313130i
$188$	−151.376	−	9.13083i	−0.805194	−	0.0485682i
$189$		0			0
$190$	−25.3401	+	23.8577i	−0.133369	+	0.125567i
$191$	154.550	+	89.2296i	0.809164	+	0.467171i	0.846665	−	0.532126i	$-0.178607\pi$
$191$	154.550	+	89.2296i	0.809164	+	0.467171i	−0.0375017	+	0.999297i	$0.511940\pi$
$192$	−314.854	+	112.390i	−1.63987	+	0.585366i
$193$	−110.794	−	191.901i	−0.574062	−	0.994304i	−0.996143	−	0.0877458i	$-0.972034\pi$
$193$	−110.794	−	191.901i	−0.574062	−	0.994304i	0.422081	−	0.906558i	$-0.361300\pi$
$194$	24.3056	−	5.73400i	0.125287	−	0.0295567i
$195$	−79.1198			−0.405742
$196$		0			0
$197$		−	242.298i		−	1.22994i	−0.788550	−	0.614970i	$-0.789168\pi$
$197$		−	242.298i		−	1.22994i	0.788550	−	0.614970i	$-0.210832\pi$
$198$	−349.081	+	82.3526i	−1.76304	+	0.415922i
$199$	257.250	−	148.523i	1.29271	−	0.746349i	0.313580	−	0.949562i	$-0.398472\pi$
$199$	257.250	−	148.523i	1.29271	−	0.746349i	0.979135	+	0.203213i	$0.0651384\pi$
$200$	−107.276	−	39.4226i	−0.536381	−	0.197113i
$201$	−81.2329	+	140.699i	−0.404144	+	0.699997i
$202$	−99.1289	+	93.3297i	−0.490737	+	0.462028i
$203$		0			0
$204$	8.67361	−	143.796i	0.0425177	−	0.704884i
$205$	−344.955	−	199.160i	−1.68271	−	0.971512i
$206$	111.654	+	33.5528i	0.542008	+	0.162877i
$207$	678.325	−	391.631i	3.27693	−	1.89194i
$208$	−30.9179	−	23.2169i	−0.148644	−	0.111620i
$209$	−27.2275			−0.130275
$210$		0			0
$211$	−141.020			−0.668341			−0.334171	−	0.942513i	$-0.608456\pi$
$211$	−141.020			−0.668341			−0.334171	+	0.942513i	$0.608456\pi$
$212$	−120.533	+	182.439i	−0.568554	+	0.860563i
$213$	104.633	−	60.4098i	0.491234	−	0.283614i
$214$	78.2038	−	260.239i	0.365439	−	1.21607i
$215$	−191.822	−	110.748i	−0.892194	−	0.515109i
$216$	−298.048	+	248.521i	−1.37985	+	1.15056i
$217$		0			0
$218$	−64.7966	+	61.0059i	−0.297232	+	0.279844i
$219$	−180.810	+	313.171i	−0.825614	+	1.43001i
$220$	−109.893	−	219.948i	−0.499514	−	0.999765i
$221$	14.4287	−	8.33040i	0.0652882	−	0.0376941i
$222$	0.486121	+	2.06060i	0.00218973	+	0.00928198i
$223$			40.8267i			0.183079i	0.995801	+	0.0915396i	$0.0291788\pi$
$223$			40.8267i			0.183079i	−0.995801	+	0.0915396i	$0.970821\pi$
$224$		0			0
$225$	−261.244			−1.16108
$226$	259.654	−	61.2555i	1.14891	−	0.271042i
$227$	4.09299	+	7.08926i	0.0180308	+	0.0312302i	0.874900	−	0.484304i	$-0.160927\pi$
$227$	4.09299	+	7.08926i	0.0180308	+	0.0312302i	−0.856869	+	0.515534i	$0.827594\pi$
$228$	−51.8942	+	25.9280i	−0.227606	+	0.113719i
$229$	−287.738	−	166.126i	−1.25650	−	0.725440i	−0.284107	−	0.958792i	$-0.591697\pi$
$229$	−287.738	−	166.126i	−1.25650	−	0.725440i	−0.972392	+	0.233352i	$0.925031\pi$
$230$	368.071	+	390.942i	1.60031	+	1.69975i
$231$		0			0
$232$	191.356	+	229.492i	0.824812	+	0.989188i
$233$	−164.630	+	285.148i	−0.706568	+	1.22381i	0.259555	+	0.965728i	$0.416424\pi$
$233$	−164.630	+	285.148i	−0.706568	+	1.22381i	−0.966123	+	0.258083i	$0.916909\pi$
$234$	−84.6397	−	25.4349i	−0.361708	−	0.108696i
$235$	−118.817	−	205.797i	−0.505603	−	0.875730i
$236$	349.742	+	231.067i	1.48196	+	0.979096i
$237$			104.122i			0.439333i
$238$		0			0
$239$			137.719i			0.576230i	0.957596	+	0.288115i	$0.0930286\pi$
$239$			137.719i			0.576230i	−0.957596	+	0.288115i	$0.906971\pi$
$240$	−418.901	−	314.561i	−1.74542	−	1.31067i
$241$	100.927	+	174.810i	0.418783	+	0.725354i	0.995817	−	0.0913661i	$-0.0291234\pi$
$241$	100.927	+	174.810i	0.418783	+	0.725354i	−0.577034	+	0.816720i	$0.695790\pi$
$242$	−14.2890	+	47.5496i	−0.0590454	+	0.196486i
$243$	−13.6746	+	23.6851i	−0.0562741	+	0.0974696i
$244$	174.750	+	10.5407i	0.716188	+	0.0431995i
$245$		0			0
$246$	−455.108	−	483.387i	−1.85003	−	1.96499i
$247$	−5.81032	−	3.35459i	−0.0235235	−	0.0135813i
$248$	−19.7808	+	53.8273i	−0.0797614	+	0.217045i
$249$	−13.3625	−	23.1445i	−0.0536647	−	0.0929499i
$250$	30.8375	+	130.716i	0.123350	+	0.522864i
$251$	269.203			1.07252			0.536261	−	0.844052i	$-0.319836\pi$
$251$	269.203			1.07252			0.536261	+	0.844052i	$0.319836\pi$
$252$		0			0
$253$			420.061i			1.66032i
$254$	60.1470	+	254.955i	0.236799	+	1.00376i
$255$	195.492	−	112.867i	0.766633	−	0.442616i
$256$	−71.3904	−	245.844i	−0.278869	−	0.960329i
$257$	−121.180	+	209.889i	−0.471516	+	0.816690i	−0.999469	−	0.0325840i	$-0.989626\pi$
$257$	−121.180	+	209.889i	−0.471516	+	0.816690i	0.527953	+	0.849274i	$0.322960\pi$
$258$	−253.075	−	268.800i	−0.980912	−	1.04186i
$259$		0			0
$260$	3.64784	−	60.4761i	0.0140302	−	0.232600i
$261$	591.498	+	341.501i	2.26627	+	1.30843i
$262$	30.6967	−	102.150i	0.117163	−	0.389884i
$263$	−29.3124	+	16.9235i	−0.111454	+	0.0643479i	−0.554691	−	0.832057i	$-0.687163\pi$
$263$	−29.3124	+	16.9235i	−0.111454	+	0.0643479i	0.443237	+	0.896405i	$0.353830\pi$
$264$	−69.9122	−	403.813i	−0.264819	−	1.52959i
$265$	−342.634			−1.29296
$266$		0			0
$267$	93.9673			0.351937
$268$	−103.800	−	68.5783i	−0.387314	−	0.255889i
$269$	143.412	−	82.7990i	0.533130	−	0.307803i	−0.209160	−	0.977881i	$-0.567073\pi$
$269$	143.412	−	82.7990i	0.533130	−	0.307803i	0.742290	+	0.670078i	$0.233740\pi$
$270$	−582.361	−	175.004i	−2.15689	−	0.648163i
$271$	−128.439	−	74.1542i	−0.473944	−	0.273632i	0.243945	−	0.969789i	$-0.421558\pi$
$271$	−128.439	−	74.1542i	−0.473944	−	0.273632i	−0.717889	+	0.696157i	$0.754892\pi$
$272$	109.513	+	13.2595i	0.402620	+	0.0487483i
$273$		0			0
$274$	−79.1300	−	84.0468i	−0.288796	−	0.306740i
$275$	70.0521	−	121.334i	0.254735	−	0.441214i
$276$	400.011	+	800.612i	1.44932	+	2.90077i
$277$	414.270	−	239.179i	1.49556	−	0.863463i	0.495574	−	0.868566i	$-0.334958\pi$
$277$	414.270	−	239.179i	1.49556	−	0.863463i	0.999987	+	0.00510300i	$0.00162434\pi$
$278$	−335.631	+	79.1796i	−1.20731	+	0.284819i
$279$			131.083i			0.469830i
$280$		0			0
$281$	−226.066			−0.804506			−0.402253	−	0.915528i	$-0.631773\pi$
$281$	−226.066			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$282$	−90.9451	−	385.504i	−0.322500	−	1.36703i
$283$	−127.314	−	220.514i	−0.449873	−	0.779202i	0.548505	−	0.836147i	$-0.315197\pi$
$283$	−127.314	−	220.514i	−0.449873	−	0.779202i	−0.998377	+	0.0569453i	$0.981864\pi$
$284$	41.3508	+	82.7625i	0.145601	+	0.291417i
$285$	−78.7229	−	45.4507i	−0.276221	−	0.159476i
$286$	34.5091	−	32.4903i	0.120661	−	0.113602i
$287$		0			0
$288$	−347.003	−	471.172i	−1.20487	−	1.63602i
$289$	120.733	−	209.115i	0.417760	−	0.723582i
$290$	−134.750	+	448.407i	−0.464654	+	1.54623i
$291$	32.6122	+	56.4860i	0.112069	+	0.194110i
$292$	−231.040	−	152.643i	−0.791232	−	0.522749i
$293$		−	149.558i		−	0.510437i	−0.966883	−	0.255218i	$-0.917853\pi$
$293$		−	149.558i		−	0.510437i	0.966883	−	0.255218i	$-0.0821474\pi$
$294$		0			0
$295$			656.842i			2.22658i
$296$	−1.59746	+	0.276568i	−0.00539681	+	0.000934351i
$297$	−237.858	−	411.981i	−0.800867	−	1.38714i
$298$	420.482	+	126.358i	1.41101	+	0.424020i
$299$	−51.7539	+	89.6403i	−0.173090	+	0.299800i
$300$	17.9728	−	297.964i	0.0599094	−	0.993214i
$301$		0			0
$302$	270.363	−	254.547i	0.895243	−	0.842870i
$303$	−307.959	−	177.800i	−1.01637	−	0.586799i
$304$	−17.4258	−	40.8613i	−0.0573216	−	0.134412i
$305$	137.163	+	237.573i	0.449714	+	0.778927i
$306$	245.414	−	57.8963i	0.802007	−	0.189203i
$307$	−271.779			−0.885272			−0.442636	−	0.896701i	$-0.645957\pi$
$307$	−271.779			−0.885272			−0.442636	+	0.896701i	$0.645957\pi$
$308$		0			0
$309$			304.502i			0.985442i
$310$	−87.4599	+	20.6329i	−0.282129	+	0.0665577i
$311$	−462.614	+	267.090i	−1.48750	+	0.858811i	−0.999898	−	0.0142534i	$-0.995463\pi$
$311$	−462.614	+	267.090i	−1.48750	+	0.858811i	−0.487605	+	0.873064i	$0.662130\pi$
$312$	34.8329	−	94.7867i	0.111644	−	0.303804i
$313$	−278.116	+	481.711i	−0.888550	+	1.53901i	−0.0469600	+	0.998897i	$0.514953\pi$
$313$	−278.116	+	481.711i	−0.888550	+	1.53901i	−0.841590	+	0.540117i	$0.818380\pi$
$314$	−274.024	+	257.993i	−0.872688	+	0.821634i
$315$		0			0
$316$	−79.5867	−	4.80057i	−0.251857	−	0.0151917i
$317$	335.549	+	193.730i	1.05852	+	0.611134i	0.925021	−	0.379916i	$-0.124047\pi$
$317$	335.549	+	193.730i	1.05852	+	0.611134i	0.133494	+	0.991050i	$0.457380\pi$
$318$	−546.939	−	164.359i	−1.71993	−	0.516853i
$319$	−317.218	+	183.146i	−0.994413	+	0.574125i
$320$	259.752	−	305.689i	0.811725	−	0.955277i
$321$	709.724			2.21098
$322$		0			0
$323$	19.1417			0.0592624
$324$	−296.403	−	195.826i	−0.914823	−	0.604403i
$325$	29.8980	−	17.2616i	0.0919940	−	0.0531127i
$326$	31.3784	−	104.418i	0.0962526	−	0.320300i
$327$	−201.300	−	116.221i	−0.615597	−	0.355415i
$328$	390.465	−	325.581i	1.19044	−	0.992624i
$329$		0			0
$330$	467.557	−	440.205i	1.41684	−	1.33395i
$331$	191.603	−	331.865i	0.578860	−	1.00261i	−0.416751	−	0.909021i	$-0.636831\pi$
$331$	191.603	−	331.865i	0.578860	−	1.00261i	0.995610	−	0.0935935i	$-0.0298354\pi$
$332$	18.3069	−	9.14670i	0.0551412	−	0.0275503i
$333$	−3.20929	+	1.85288i	−0.00963750	+	0.00556422i
$334$	122.352	+	518.633i	0.366323	+	1.55279i
$335$		−	194.944i		−	0.581923i
$336$		0			0
$337$	563.726			1.67278			0.836388	−	0.548138i	$-0.184663\pi$
$337$	563.726			1.67278			0.836388	+	0.548138i	$0.184663\pi$
$338$	−317.602	+	74.9264i	−0.939652	+	0.221676i
$339$	348.392	+	603.432i	1.02770	+	1.78004i
$340$	77.2581	+	154.630i	0.227230	+	0.454794i
$341$	−60.8809	−	35.1496i	−0.178536	−	0.103078i
$342$	−69.6040	−	73.9289i	−0.203520	−	0.216166i
$343$		0			0
$344$	217.129	−	181.048i	0.631188	−	0.526302i
$345$	−701.203	+	1214.52i	−2.03247	+	3.52035i
$346$	−219.953	−	66.0976i	−0.635703	−	0.191034i
$347$	−25.7945	−	44.6774i	−0.0743357	−	0.128753i	0.826462	−	0.562993i	$-0.190350\pi$
$347$	−25.7945	−	44.6774i	−0.0743357	−	0.128753i	−0.900797	+	0.434240i	$0.857017\pi$
$348$	−430.195	+	651.143i	−1.23619	+	1.87110i
$349$			586.383i			1.68018i	0.542447	+	0.840090i	$0.317498\pi$
$349$			586.383i			1.68018i	−0.542447	+	0.840090i	$0.682502\pi$
$350$		0			0
$351$		−	117.222i		−	0.333965i
$352$	311.882	−	34.8203i	0.886030	−	0.0989213i
$353$	151.922	+	263.136i	0.430373	+	0.745428i	0.996905	−	0.0786114i	$-0.0250486\pi$
$353$	151.922	+	263.136i	0.430373	+	0.745428i	−0.566532	+	0.824040i	$0.691715\pi$
$354$	−315.082	+	1048.50i	−0.890063	+	2.96187i
$355$	−72.4862	+	125.550i	−0.204187	+	0.353661i
$356$	−4.33239	+	71.8250i	−0.0121696	+	0.201756i
$357$		0			0
$358$	154.713	+	164.326i	0.432159	+	0.459012i
$359$	−100.571	−	58.0649i	−0.280143	−	0.161741i	0.353345	−	0.935493i	$-0.385044\pi$
$359$	−100.571	−	58.0649i	−0.280143	−	0.161741i	−0.633488	+	0.773752i	$0.718377\pi$
$360$	316.280	−	860.657i	0.878557	−	2.39071i
$361$	176.646	+	305.960i	0.489324	+	0.847534i
$362$	27.9880	+	118.637i	0.0773150	+	0.327727i
$363$	−129.677			−0.357237
$364$		0			0
$365$		−	433.910i		−	1.18879i
$366$	104.988	+	445.027i	0.286851	+	1.21592i
$367$	412.478	−	238.144i	1.12392	−	0.648894i	0.181520	−	0.983387i	$-0.441898\pi$
$367$	412.478	−	238.144i	1.12392	−	0.648894i	0.942398	+	0.334493i	$0.108565\pi$
$368$	−630.400	+	268.841i	−1.71304	+	0.730546i
$369$	581.042	−	1006.39i	1.57464	−	2.72736i
$370$	−1.74142	−	1.84962i	−0.00470654	−	0.00499898i
$371$		0			0
$372$	−149.507	−	9.01809i	−0.401902	−	0.0242422i
$373$	−42.6827	−	24.6428i	−0.114431	−	0.0660666i	0.441692	−	0.897167i	$-0.354378\pi$
$373$	−42.6827	−	24.6428i	−0.114431	−	0.0660666i	−0.556123	+	0.831100i	$0.687712\pi$
$374$	−38.9176	+	129.506i	−0.104058	+	0.346274i
$375$	−303.782	+	175.389i	−0.810086	+	0.467704i
$376$	298.857	−	51.7412i	0.794833	−	0.137610i
$377$	−90.2585			−0.239412
$378$		0			0
$379$	167.511			0.441983			0.220991	−	0.975276i	$-0.429071\pi$
$379$	167.511			0.441983			0.220991	+	0.975276i	$0.429071\pi$
$380$	38.3703	−	58.0772i	0.100974	−	0.152835i
$381$	−592.512	+	342.087i	−1.55515	+	0.897866i
$382$	−341.818	−	102.719i	−0.894812	−	0.268898i
$383$	−444.450	−	256.604i	−1.16044	−	0.669983i	−0.209034	−	0.977908i	$-0.567032\pi$
$383$	−444.450	−	256.604i	−1.16044	−	0.669983i	−0.951411	+	0.307925i	$0.900365\pi$
$384$	561.273	−	363.362i	1.46165	−	0.946256i
$385$		0			0
$386$	303.792	+	322.668i	0.787026	+	0.835929i
$387$	323.104	−	559.633i	0.834895	−	1.44608i
$388$	−44.6793	+	22.3232i	−0.115153	+	0.0575341i
$389$	614.357	−	354.699i	1.57932	−	0.911823i	0.584370	−	0.811487i	$-0.301342\pi$
$389$	614.357	−	354.699i	1.57932	−	0.911823i	0.994954	−	0.100336i	$-0.0319916\pi$
$390$	154.012	−	36.3333i	0.394902	−	0.0931623i
$391$		−	295.315i		−	0.755281i
$392$		0			0
$393$	278.582			0.708860
$394$	111.268	+	471.649i	0.282406	+	1.19708i
$395$	−62.4683	−	108.198i	−0.158148	−	0.273920i
$396$	641.691	−	320.609i	1.62043	−	0.809620i
$397$	267.952	+	154.702i	0.674941	+	0.389677i	0.797946	−	0.602729i	$-0.205920\pi$
$397$	267.952	+	154.702i	0.674941	+	0.389677i	−0.123005	+	0.992406i	$0.539253\pi$
$398$	−432.549	+	407.245i	−1.08681	+	1.02323i
$399$		0			0
$400$	226.924	+	27.4754i	0.567309	+	0.0686886i
$401$	264.036	−	457.324i	0.658445	−	1.14046i	−0.322574	−	0.946544i	$-0.604548\pi$
$401$	264.036	−	457.324i	0.658445	−	1.14046i	0.981018	−	0.193915i	$-0.0621186\pi$
$402$	93.5132	−	311.184i	0.232620	−	0.774091i
$403$	−8.66126	−	15.0017i	−0.0214920	−	0.0372252i
$404$	150.102	−	227.194i	0.371540	−	0.562362i
$405$		−	556.666i		−	1.37448i
$406$		0			0
$407$		−	1.98739i		−	0.00488302i
$408$	49.1503	+	283.892i	0.120466	+	0.695814i
$409$	−306.415	−	530.726i	−0.749181	−	1.29762i	−0.948216	−	0.317627i	$-0.897114\pi$
$409$	−306.415	−	530.726i	−0.749181	−	1.29762i	0.199035	−	0.979992i	$-0.436219\pi$
$410$	762.936	+	229.268i	1.86082	+	0.559190i
$411$	150.748	−	261.104i	0.366785	−	0.635290i
$412$	−232.749	−	14.0391i	−0.564926	−	0.0340756i
$413$		0			0
$414$	−1140.56	+	1073.84i	−2.75497	+	2.59381i
$415$	27.7713	+	16.0338i	0.0669188	+	0.0386356i
$416$	70.8453	+	30.9951i	0.170301	+	0.0745075i
$417$	−450.335	−	780.003i	−1.07994	−	1.87051i
$418$	53.0002	−	12.5034i	0.126795	−	0.0299124i
$419$	237.642			0.567165			0.283583	−	0.958948i	$-0.408477\pi$
$419$	237.642			0.567165			0.283583	+	0.958948i	$0.408477\pi$
$420$		0			0
$421$		−	394.516i		−	0.937092i	−0.883439	−	0.468546i	$-0.844778\pi$
$421$		−	394.516i		−	0.937092i	0.883439	−	0.468546i	$-0.155222\pi$
$422$	274.505	−	64.7591i	0.650485	−	0.153458i
$423$	600.404	−	346.644i	1.41940	−	0.819488i
$424$	150.847	−	410.481i	0.355770	−	0.968116i
$425$	−49.2487	+	85.3012i	−0.115879	+	0.200709i
$426$	−175.933	+	165.641i	−0.412989	+	0.388829i
$427$		0			0
$428$	−32.7220	+	542.486i	−0.0764533	+	1.26749i
$429$	107.208	+	61.8964i	0.249901	+	0.144281i
$430$	424.252	+	127.491i	0.986631	+	0.296490i
$431$	−314.678	+	181.679i	−0.730111	+	0.421530i	−0.818463	−	0.574560i	$-0.805173\pi$
$431$	−314.678	+	181.679i	−0.730111	+	0.421530i	0.0883519	+	0.996089i	$0.471840\pi$
$432$	466.045	−	620.632i	1.07881	−	1.43665i
$433$	−119.733			−0.276520			−0.138260	−	0.990396i	$-0.544151\pi$
$433$	−119.733			−0.276520			−0.138260	+	0.990396i	$0.544151\pi$
$434$		0			0
$435$	−1222.89			−2.81125
$436$	98.1157	−	148.508i	0.225036	−	0.340614i
$437$	−102.989	+	59.4605i	−0.235672	+	0.136065i
$438$	208.143	−	692.640i	0.475213	−	1.58137i
$439$	754.721	+	435.738i	1.71918	+	0.992570i	0.920427	+	0.390914i	$0.127841\pi$
$439$	754.721	+	435.738i	1.71918	+	0.992570i	0.798755	+	0.601657i	$0.205492\pi$
$440$	314.919	+	377.679i	0.715724	+	0.858361i
$441$		0			0
$442$	−24.2609	+	22.8416i	−0.0548889	+	0.0516778i
$443$	171.978	−	297.875i	0.388212	−	0.672403i	−0.603997	−	0.796987i	$-0.706426\pi$
$443$	171.978	−	297.875i	0.388212	−	0.672403i	0.992209	+	0.124584i	$0.0397595\pi$
$444$	−1.89253	−	3.78785i	−0.00426246	−	0.00853120i
$445$	−97.6462	+	56.3761i	−0.219430	+	0.126688i
$446$	−18.7484	−	79.4718i	−0.0420367	−	0.178188i
$447$			1146.74i			2.56541i
$448$		0			0
$449$	−242.849			−0.540866			−0.270433	−	0.962739i	$-0.587167\pi$
$449$	−242.849			−0.540866			−0.270433	+	0.962739i	$0.587167\pi$
$450$	508.529	−	119.968i	1.13006	−	0.266596i
$451$	311.611	+	539.726i	0.690933	+	1.19673i
$452$	−477.303	+	238.476i	−1.05598	+	0.527601i
$453$	839.924	+	484.930i	1.85414	+	1.07049i
$454$	−11.2228	−	11.9201i	−0.0247198	−	0.0262558i
$455$		0			0
$456$	89.1088	−	74.3013i	0.195414	−	0.162942i
$457$	21.1285	−	36.5957i	0.0462331	−	0.0800781i	−0.841983	−	0.539504i	$-0.818612\pi$
$457$	21.1285	−	36.5957i	0.0462331	−	0.0800781i	0.888216	+	0.459426i	$0.151945\pi$
$458$	636.390	+	191.240i	1.38950	+	0.417554i
$459$	167.221	+	289.635i	0.364315	+	0.631013i
$460$	−896.003	−	591.969i	−1.94783	−	1.28689i
$461$		−	816.370i		−	1.77087i	−0.464766	−	0.885434i	$-0.653861\pi$
$461$		−	816.370i		−	1.77087i	0.464766	−	0.885434i	$-0.346139\pi$
$462$		0			0
$463$			115.161i			0.248727i	0.992237	+	0.124363i	$0.0396889\pi$
$463$			115.161i			0.248727i	−0.992237	+	0.124363i	$0.960311\pi$
$464$	−477.875	−	358.846i	−1.02990	−	0.773375i
$465$	−117.350	−	203.256i	−0.252365	−	0.437109i
$466$	189.518	−	630.661i	0.406691	−	1.35335i
$467$	301.712	−	522.580i	0.646064	−	1.11902i	−0.337991	−	0.941149i	$-0.609747\pi$
$467$	301.712	−	522.580i	0.646064	−	1.11902i	0.984055	−	0.177866i	$-0.0569194\pi$
$468$	176.437	+	10.6424i	0.377002	+	0.0227403i
$469$		0			0
$470$	325.790	+	346.034i	0.693171	+	0.736242i
$471$	−851.296	−	491.496i	−1.80742	−	1.04352i
$472$	−786.907	−	289.178i	−1.66718	−	0.612666i
$473$	173.280	+	300.129i	0.366342	+	0.634523i
$474$	−47.8147	−	202.680i	−0.100875	−	0.427595i
$475$	39.6641			0.0835034
$476$		0			0
$477$		−	999.624i		−	2.09565i
$478$	−63.2432	−	268.079i	−0.132308	−	0.560835i
$479$	−137.348	+	79.2977i	−0.286738	+	0.165548i	−0.636470	−	0.771302i	$-0.719606\pi$
$479$	−137.348	+	79.2977i	−0.286738	+	0.165548i	0.349732	+	0.936850i	$0.386273\pi$
$480$	959.870	+	419.947i	1.99973	+	0.874889i
$481$	0.244858	−	0.424106i	0.000509060	−	0.000881717i
$482$	−276.737	−	293.932i	−0.574143	−	0.609818i
$483$		0			0
$484$	5.97880	−	99.1201i	0.0123529	−	0.204794i
$485$	−67.7780	−	39.1317i	−0.139749	−	0.0806838i
$486$	15.7419	−	52.3843i	0.0323906	−	0.107787i
$487$	−92.6539	+	53.4937i	−0.190254	+	0.109843i	−0.592102	−	0.805863i	$-0.701702\pi$
$487$	−92.6539	+	53.4937i	−0.190254	+	0.109843i	0.401847	+	0.915707i	$0.368368\pi$
$488$	−345.002	+	59.7303i	−0.706972	+	0.122398i
$489$	284.768			0.582348
$490$		0			0
$491$	616.591			1.25579			0.627893	−	0.778299i	$-0.283917\pi$
$491$	616.591			1.25579			0.627893	+	0.778299i	$0.283917\pi$
$492$	1107.88	+	731.950i	2.25179	+	1.48770i
$493$	223.013	−	128.757i	0.452360	−	0.261170i
$494$	12.8507	+	3.86172i	0.0260135	+	0.00781724i
$495$	973.438	+	562.015i	1.96654	+	1.13538i
$496$	13.7862	−	113.862i	0.0277947	−	0.229561i
$497$		0			0
$498$	36.6394	+	38.9160i	0.0735731	+	0.0781446i
$499$	−277.045	+	479.856i	−0.555200	+	0.961635i	0.442688	+	0.896676i	$0.354025\pi$
$499$	−277.045	+	479.856i	−0.555200	+	0.961635i	−0.997888	+	0.0649593i	$0.979308\pi$
$500$	−120.055	−	240.286i	−0.240109	−	0.480572i
$501$	−1205.30	+	695.879i	−2.40578	+	1.38898i
$502$	−524.022	+	123.623i	−1.04387	+	0.246261i
$503$		−	148.158i		−	0.294548i	−0.989096	−	0.147274i	$-0.952950\pi$
$503$		−	148.158i		−	0.294548i	0.989096	−	0.147274i	$-0.0470499\pi$
$504$		0			0
$505$	426.688			0.844926
$506$	−192.900	−	817.675i	−0.381225	−	1.61596i
$507$	−426.145	−	738.104i	−0.840522	−	1.45583i
$508$	−234.160	−	468.666i	−0.460946	−	0.922570i
$509$	−158.386	−	91.4444i	−0.311172	−	0.179655i	0.336279	−	0.941762i	$-0.390831\pi$
$509$	−158.386	−	91.4444i	−0.311172	−	0.179655i	−0.647451	+	0.762107i	$0.724165\pi$
$510$	−328.706	+	309.477i	−0.644522	+	0.606817i
$511$		0			0
$512$	251.863	+	445.768i	0.491919	+	0.870641i
$513$	67.3385	−	116.634i	0.131264	−	0.227356i
$514$	139.499	−	464.211i	0.271399	−	0.903134i
$515$	−182.687	−	316.423i	−0.354732	−	0.614414i
$516$	616.066	+	407.021i	1.19393	+	0.788800i
$517$			371.807i			0.719163i
$518$		0			0
$519$		−	599.856i		−	1.15579i
$520$	20.6710	+	119.396i	0.0397520	+	0.229607i
$521$	49.1230	+	85.0836i	0.0942861	+	0.163308i	0.909310	−	0.416118i	$-0.136610\pi$
$521$	49.1230	+	85.0836i	0.0942861	+	0.163308i	−0.815024	+	0.579427i	$0.803277\pi$
$522$	−1308.21	−	393.128i	−2.50615	−	0.753118i
$523$	−287.382	+	497.760i	−0.549488	+	0.951740i	0.448822	+	0.893621i	$0.351844\pi$
$523$	−287.382	+	497.760i	−0.549488	+	0.951740i	−0.998310	+	0.0581192i	$0.981490\pi$
$524$	−12.8441	+	212.937i	−0.0245116	+	0.406369i
$525$		0			0
$526$	49.2868	−	46.4035i	0.0937012	−	0.0882196i
$527$	42.8010	+	24.7112i	0.0812163	+	0.0468903i
$528$	321.527	+	753.943i	0.608953	+	1.42792i
$529$	652.843	+	1130.76i	1.23411	+	2.13754i
$530$	666.960	−	157.344i	1.25842	−	0.296876i
$531$	−1916.31			−3.60888
$532$		0			0
$533$			153.569i			0.288122i
$534$	−182.914	+	43.1516i	−0.342535	+	0.0808082i
$535$	−737.510	+	425.802i	−1.37852	+	0.795891i
$536$	233.546	+	85.8252i	0.435720	+	0.160122i
$537$	−294.740	+	510.504i	−0.548864	+	0.950660i
$538$	−241.138	+	227.031i	−0.448212	+	0.421991i
$539$		0			0
$540$	1213.97	+	73.2251i	2.24809	+	0.135602i
$541$	320.996	+	185.327i	0.593338	+	0.342564i	0.766416	−	0.642344i	$-0.222038\pi$
$541$	320.996	+	185.327i	0.593338	+	0.342564i	−0.173078	+	0.984908i	$0.555371\pi$
$542$	284.068	+	85.3644i	0.524110	+	0.157499i
$543$	−275.712	+	159.182i	−0.507756	+	0.293153i
$544$	−219.262	+	24.4797i	−0.403056	+	0.0449994i
$545$	278.909			0.511759
$546$		0			0
$547$	−56.5966			−0.103467			−0.0517336	−	0.998661i	$-0.516475\pi$
$547$	−56.5966			−0.103467			−0.0517336	+	0.998661i	$0.516475\pi$
$548$	192.628	+	127.265i	0.351510	+	0.232235i
$549$	−693.110	+	400.167i	−1.26250	+	0.728902i
$550$	−80.6422	+	268.353i	−0.146622	+	0.487915i
$551$	−89.8057	−	51.8494i	−0.162987	−	0.0941005i
$552$	−1146.31	−	1374.75i	−2.07664	−	2.49049i
$553$		0			0
$554$	−696.569	+	655.819i	−1.25734	+	1.18379i
$555$	3.31753	−	5.74613i	0.00597753	−	0.0103534i
$556$	616.968	−	308.257i	1.10965	−	0.554418i
$557$	−131.224	+	75.7624i	−0.235591	+	0.136019i	−0.613149	−	0.789968i	$-0.710097\pi$
$557$	−131.224	+	75.7624i	−0.235591	+	0.136019i	0.377558	+	0.925986i	$0.376764\pi$
$558$	−60.1957	−	255.161i	−0.107878	−	0.457278i
$559$			85.3962i			0.152766i
$560$		0			0
$561$	−353.189			−0.629571
$562$	440.053	−	103.814i	0.783012	−	0.184722i
$563$	−159.024	−	275.438i	−0.282458	−	0.489232i	0.689531	−	0.724256i	$-0.257817\pi$
$563$	−159.024	−	275.438i	−0.282458	−	0.489232i	−0.971990	+	0.235024i	$0.924483\pi$
$564$	354.061	+	708.644i	0.627768	+	1.25646i
$565$	−724.063	−	418.038i	−1.28153	−	0.739891i
$566$	349.089	+	370.780i	0.616766	+	0.655089i
$567$		0			0
$568$	−118.498	−	142.114i	−0.208624	−	0.250200i
$569$	−178.327	+	308.871i	−0.313404	+	0.542831i	−0.979097	−	0.203394i	$-0.934803\pi$
$569$	−178.327	+	308.871i	−0.313404	+	0.542831i	0.665693	+	0.746226i	$0.268136\pi$
$570$	174.111	+	52.3217i	0.305458	+	0.0917924i
$571$	−415.507	−	719.679i	−0.727683	−	1.26038i	−0.957860	−	0.287235i	$-0.907264\pi$
$571$	−415.507	−	719.679i	−0.727683	−	1.26038i	0.230177	−	0.973149i	$-0.426069\pi$
$572$	−52.2541	+	79.0917i	−0.0913533	+	0.138272i
$573$		−	932.205i		−	1.62689i
$574$		0			0
$575$		−	611.929i		−	1.06422i
$576$	891.836	+	757.818i	1.54833	+	1.31566i
$577$	385.742	+	668.124i	0.668530	+	1.15793i	0.978315	+	0.207121i	$0.0664094\pi$
$577$	385.742	+	668.124i	0.668530	+	1.15793i	−0.309786	+	0.950806i	$0.600257\pi$
$578$	−138.985	+	462.499i	−0.240458	+	0.800172i
$579$	−578.746	+	1002.42i	−0.999562	+	1.73129i
$580$	56.3819	−	934.734i	0.0972102	−	1.61161i
$581$		0			0
$582$	−89.4212	−	94.9775i	−0.153645	−	0.163192i
$583$	464.271	+	268.047i	0.796349	+	0.459772i
$584$	519.831	+	191.031i	0.890121	+	0.327108i
$585$	138.487	+	239.866i	0.236730	+	0.410028i
$586$	68.6799	+	291.124i	0.117201	+	0.496799i
$587$	−144.376			−0.245956			−0.122978	−	0.992409i	$-0.539244\pi$
$587$	−144.376			−0.245956			−0.122978	+	0.992409i	$0.539244\pi$
$588$		0			0
$589$		−	19.9020i		−	0.0337894i
$590$	−301.634	−	1278.59i	−0.511245	−	2.16709i
$591$	−1096.11	+	632.838i	−1.85467	+	1.07079i
$592$	2.98255	−	1.27194i	0.00503809	−	0.00214855i
$593$	419.463	−	726.531i	0.707357	−	1.22518i	−0.258477	−	0.966018i	$-0.583220\pi$
$593$	419.463	−	726.531i	0.707357	−	1.22518i	0.965834	−	0.259162i	$-0.0834462\pi$
$594$	652.195	+	692.720i	1.09797	+	1.16620i
$595$		0			0
$596$	−876.521	−	52.8706i	−1.47067	−	0.0887090i
$597$	−1343.78	−	775.831i	−2.25089	−	1.29955i
$598$	59.5777	−	198.257i	0.0996283	−	0.331534i
$599$	616.039	−	355.670i	1.02845	−	0.593774i	0.111907	−	0.993719i	$-0.464304\pi$
$599$	616.039	−	355.670i	1.02845	−	0.593774i	0.916539	+	0.399945i	$0.130971\pi$
$600$	101.846	+	588.260i	0.169743	+	0.980434i
$601$	356.394			0.593002			0.296501	−	0.955033i	$-0.404180\pi$
$601$	356.394			0.593002			0.296501	+	0.955033i	$0.404180\pi$
$602$		0			0
$603$	568.742			0.943188
$604$	−409.387	+	619.648i	−0.677793	+	1.02591i
$605$	134.754	−	77.8003i	0.222734	−	0.128596i
$606$	681.111	+	204.679i	1.12395	+	0.337754i
$607$	52.2836	+	30.1860i	0.0861345	+	0.0497298i	0.542449	−	0.840089i	$-0.317497\pi$
$607$	52.2836	+	30.1860i	0.0861345	+	0.0497298i	−0.456314	+	0.889819i	$0.650831\pi$
$608$	52.6847	+	71.5370i	0.0866525	+	0.117660i
$609$		0			0
$610$	−376.094	−	399.463i	−0.616548	−	0.654858i
$611$	−45.8088	+	79.3431i	−0.0749735	+	0.129858i
$612$	−451.128	+	225.398i	−0.737136	+	0.368297i
$613$	418.281	−	241.495i	0.682351	−	0.393955i	−0.118389	−	0.992967i	$-0.537773\pi$
$613$	418.281	−	241.495i	0.682351	−	0.393955i	0.800740	+	0.599012i	$0.204440\pi$
$614$	529.035	−	124.806i	0.861621	−	0.203267i
$615$			2080.68i			3.38321i
$616$		0			0
$617$	712.490			1.15476			0.577382	−	0.816474i	$-0.304074\pi$
$617$	712.490			1.15476			0.577382	+	0.816474i	$0.304074\pi$
$618$	−139.833	−	592.732i	−0.226267	−	0.959114i
$619$	−46.5409	−	80.6112i	−0.0751872	−	0.130228i	0.825980	−	0.563699i	$-0.190622\pi$
$619$	−46.5409	−	80.6112i	−0.0751872	−	0.130228i	−0.901168	+	0.433471i	$0.857289\pi$
$620$	160.771	−	80.3265i	0.259309	−	0.129559i
$621$	−1799.40	−	1038.88i	−2.89758	−	1.67292i
$622$	777.855	−	732.350i	1.25057	−	1.17741i
$623$		0			0
$624$	−24.2767	+	200.504i	−0.0389049	+	0.321321i
$625$	389.030	−	673.819i	0.622447	−	1.07811i
$626$	320.160	−	1065.40i	0.511438	−	1.70192i
$627$	71.1133	+	123.172i	0.113418	+	0.196446i
$628$	414.930	−	628.038i	0.660717	−	1.00006i
$629$			1.39719i			0.00222129i
$630$		0			0
$631$			610.573i			0.967628i	0.875171	+	0.483814i	$0.160749\pi$
$631$			610.573i			0.967628i	−0.875171	+	0.483814i	$0.839251\pi$
$632$	157.125	−	27.2031i	0.248616	−	0.0430429i
$633$	368.318	+	637.946i	0.581861	+	1.00781i
$634$	−742.133	−	223.016i	−1.17056	−	0.351761i
$635$	410.473	−	710.961i	0.646415	−	1.11962i
$636$	1140.13	+	68.7711i	1.79266	+	0.108131i
$637$		0			0
$638$	533.381	−	502.178i	0.836021	−	0.787113i
$639$	−366.287	−	211.476i	−0.573219	−	0.330948i
$640$	−365.246	+	714.326i	−0.570697	+	1.11613i
$641$	−295.077	−	511.088i	−0.460338	−	0.797328i	0.538640	−	0.842536i	$-0.318938\pi$
$641$	−295.077	−	511.088i	−0.460338	−	0.797328i	−0.998978	+	0.0452077i	$0.985605\pi$
$642$	−1381.52	+	325.919i	−2.15191	+	0.507662i
$643$	257.971			0.401199			0.200600	−	0.979673i	$-0.435711\pi$
$643$	257.971			0.401199			0.200600	+	0.979673i	$0.435711\pi$
$644$		0			0
$645$			1157.02i			1.79383i
$646$	−37.2607	+	8.79025i	−0.0576790	+	0.0136072i
$647$	−329.059	+	189.982i	−0.508591	+	0.293635i	−0.732254	−	0.681031i	$-0.761532\pi$
$647$	−329.059	+	189.982i	−0.508591	+	0.293635i	0.223663	+	0.974667i	$0.428198\pi$
$648$	666.895	+	245.075i	1.02916	+	0.378203i
$649$	513.856	−	890.024i	0.791765	−	1.37138i
$650$	−50.2716	+	47.3307i	−0.0773410	+	0.0728164i
$651$		0			0
$652$	−13.1293	+	217.666i	−0.0201370	+	0.333843i
$653$	825.126	+	476.386i	1.26359	+	0.729535i	0.973768	−	0.227545i	$-0.0730698\pi$
$653$	825.126	+	476.386i	1.26359	+	0.729535i	0.289824	+	0.957080i	$0.406403\pi$
$654$	445.215	+	133.790i	0.680757	+	0.204572i
$655$	−289.489	+	167.136i	−0.441968	+	0.255170i
$656$	−610.553	+	813.073i	−0.930722	+	1.23944i
$657$	1265.92			1.92681
$658$		0			0
$659$	−963.119			−1.46149			−0.730743	−	0.682653i	$-0.760826\pi$
$659$	−963.119			−1.46149			−0.730743	+	0.682653i	$0.760826\pi$
$660$	−707.981	+	1071.60i	−1.07270	+	1.62363i
$661$	−62.0782	+	35.8409i	−0.0939156	+	0.0542222i	−0.546222	−	0.837640i	$-0.683935\pi$
$661$	−62.0782	+	35.8409i	−0.0939156	+	0.0542222i	0.452307	+	0.891862i	$0.350601\pi$
$662$	−220.568	+	733.985i	−0.333184	+	1.10874i
$663$	−75.3701	−	43.5150i	−0.113680	−	0.0656334i
$664$	−31.4352	+	26.2115i	−0.0473422	+	0.0394752i
$665$		0			0
$666$	5.39621	−	5.08053i	0.00810242	−	0.00762842i
$667$	−799.921	+	1385.50i	−1.19928	+	2.07722i
$668$	−476.332	−	953.367i	−0.713072	−	1.42720i
$669$	184.692	−	106.632i	0.276071	−	0.159390i
$670$	89.5221	+	379.471i	0.133615	+	0.566375i
$671$		−	429.216i		−	0.639667i
$672$		0			0
$673$	−712.783			−1.05911			−0.529556	−	0.848275i	$-0.677642\pi$
$673$	−712.783			−1.05911			−0.529556	+	0.848275i	$0.677642\pi$
$674$	−1097.33	+	258.874i	−1.62808	+	0.384085i
$675$	346.502	+	600.160i	0.513337	+	0.889125i
$676$	583.826	−	291.698i	0.863648	−	0.431506i
$677$	664.698	+	383.763i	0.981828	+	0.566859i	0.902822	−	0.430015i	$-0.141492\pi$
$677$	664.698	+	383.763i	0.981828	+	0.566859i	0.0790065	+	0.996874i	$0.474825\pi$
$678$	−955.275	−	1014.63i	−1.40896	−	1.49651i
$679$		0			0
$680$	−221.397	−	265.519i	−0.325584	−	0.390469i
$681$	21.3803	−	37.0317i	0.0313954	−	0.0543784i
$682$	134.650	+	40.4633i	0.197434	+	0.0593304i
$683$	242.177	+	419.462i	0.354578	+	0.614147i	0.987046	−	0.160440i	$-0.0512912\pi$
$683$	242.177	+	419.462i	0.354578	+	0.614147i	−0.632468	+	0.774587i	$0.717958\pi$
$684$	169.438	+	111.944i	0.247717	+	0.163661i
$685$			361.769i			0.528130i
$686$		0			0
$687$			1735.56i			2.52629i
$688$	−339.515	+	452.131i	−0.493481	+	0.657168i
$689$	66.0499	+	114.402i	0.0958634	+	0.166040i
$690$	807.208	−	2686.15i	1.16987	−	3.89297i
$691$	−287.425	+	497.835i	−0.415956	+	0.720457i	−0.995528	−	0.0944642i	$-0.969886\pi$
$691$	−287.425	+	497.835i	−0.415956	+	0.720457i	0.579572	+	0.814921i	$0.303220\pi$
$692$	458.507	+	27.6565i	0.662582	+	0.0399661i
$693$		0			0
$694$	70.7274	+	75.1221i	0.101913	+	0.108245i
$695$	935.933	+	540.361i	1.34667	+	0.777498i
$696$	538.386	−	1465.05i	0.773543	−	2.10495i
$697$	−219.071	−	379.443i	−0.314306	−	0.544394i
$698$	−269.278	−	1141.43i	−0.385786	−	1.63529i
$699$	1719.94			2.46057
$700$		0			0
$701$		−	143.138i		−	0.204191i	−0.994775	−	0.102096i	$-0.967445\pi$
$701$		−	143.138i		−	0.204191i	0.994775	−	0.102096i	$-0.0325548\pi$
$702$	53.8304	+	228.180i	0.0766815	+	0.325042i
$703$	0.487259	−	0.281319i	0.000693114	−	0.000400169i
$704$	−591.110	+	211.002i	−0.839644	+	0.299719i
$705$	−620.655	+	1075.01i	−0.880361	+	1.52483i
$706$	−416.563	−	442.446i	−0.590032	−	0.626695i
$707$		0			0
$708$	131.837	−	2185.67i	0.186210	−	3.08710i
$709$	−221.106	−	127.656i	−0.311856	−	0.180050i	0.335901	−	0.941897i	$-0.390959\pi$
$709$	−221.106	−	127.656i	−0.311856	−	0.180050i	−0.647757	+	0.761847i	$0.724293\pi$
$710$	83.4443	−	277.678i	0.117527	−	0.391096i
$711$	315.665	−	182.249i	0.443973	−	0.256328i
$712$	−24.5501	−	141.802i	−0.0344805	−	0.199160i
$713$	−307.044			−0.430636
$714$		0			0
$715$	−148.540			−0.207748
$716$	−376.621	−	248.825i	−0.526007	−	0.347521i
$717$	623.013	−	359.697i	0.868916	−	0.501669i
$718$	222.433	+	66.8429i	0.309796	+	0.0930959i
$719$	−359.947	−	207.815i	−0.500621	−	0.289034i	0.228349	−	0.973579i	$-0.426667\pi$
$719$	−359.947	−	207.815i	−0.500621	−	0.289034i	−0.728970	+	0.684546i	$0.760001\pi$
$720$	−220.430	+	1820.57i	−0.306153	+	2.52857i
$721$		0			0
$722$	−484.355	−	514.451i	−0.670852	−	0.712537i
$723$	527.204	−	913.144i	0.729190	−	1.26299i
$724$	−108.961	−	218.083i	−0.150499	−	0.301219i
$725$	462.112	−	266.800i	0.637395	−	0.368000i
$726$	252.425	−	59.5502i	0.347693	−	0.0820250i
$727$			896.838i			1.23361i	0.787114	+	0.616807i	$0.211574\pi$
$727$			896.838i			1.23361i	−0.787114	+	0.616807i	$0.788426\pi$
$728$		0			0
$729$	−656.451			−0.900481
$730$	199.260	+	844.634i	0.272959	+	1.15703i
$731$	−121.821	−	211.000i	−0.166649	−	0.288645i
$732$	−408.730	−	818.063i	−0.558375	−	1.11757i
$733$	440.858	+	254.530i	0.601444	+	0.347244i	0.769609	−	0.638515i	$-0.220451\pi$
$733$	440.858	+	254.530i	0.601444	+	0.347244i	−0.168166	+	0.985759i	$0.553784\pi$
$734$	−693.555	+	652.981i	−0.944898	+	0.889620i
$735$		0			0
$736$	1103.66	−	812.808i	1.49954	−	1.10436i
$737$	−152.507	+	264.150i	−0.206930	+	0.358413i
$738$	−668.881	+	2225.84i	−0.906343	+	3.01604i
$739$	−370.714	−	642.095i	−0.501642	−	0.868870i	−0.999998	−	0.00189750i	$-0.999396\pi$
$739$	−370.714	−	642.095i	−0.501642	−	0.868870i	0.498356	−	0.866973i	$-0.333937\pi$
$740$	4.23917	+	2.80072i	0.00572861	+	0.00378476i
$741$			35.0463i			0.0472959i
$742$		0			0
$743$		−	1344.98i		−	1.81021i	−0.425191	−	0.905104i	$-0.639793\pi$
$743$		−	1344.98i		−	1.81021i	0.425191	−	0.905104i	$-0.360207\pi$
$744$	295.167	−	51.1024i	0.396730	−	0.0686860i
$745$	−687.989	−	1191.63i	−0.923476	−	1.59951i
$746$	94.4011	+	28.3682i	0.126543	+	0.0380271i
$747$	−46.7780	+	81.0218i	−0.0626211	+	0.108463i
$748$	16.2839	−	269.964i	0.0217699	−	0.360915i
$749$		0			0
$750$	510.790	−	480.909i	0.681054	−	0.641211i
$751$	23.9829	+	13.8465i	0.0319346	+	0.0184375i	0.515882	−	0.856659i	$-0.327464\pi$
$751$	23.9829	+	13.8465i	0.0319346	+	0.0184375i	−0.483948	+	0.875097i	$0.660798\pi$
$752$	−557.985	+	237.959i	−0.742001	+	0.316434i
$753$	−703.109	−	1217.82i	−0.933743	−	1.61729i
$754$	175.694	−	41.4484i	0.233016	−	0.0549714i
$755$	−1163.74			−1.54138
$756$		0			0
$757$		−	1341.69i		−	1.77238i	−0.463318	−	0.886192i	$-0.653341\pi$
$757$		−	1341.69i		−	1.77238i	0.463318	−	0.886192i	$-0.346659\pi$
$758$	−326.072	+	76.9244i	−0.430174	+	0.101483i
$759$	1900.27	−	1097.12i	2.50365	−	1.44548i
$760$	−48.0201	+	130.672i	−0.0631844	+	0.171936i
$761$	−56.0005	+	96.9958i	−0.0735881	+	0.127458i	−0.900471	−	0.434915i	$-0.856778\pi$
$761$	−56.0005	+	96.9958i	−0.0735881	+	0.127458i	0.826883	+	0.562374i	$0.190112\pi$
$762$	996.271	−	937.988i	1.30744	−	1.23096i
$763$		0			0
$764$	712.542	+	42.9796i	0.932647	+	0.0562560i
$765$	−684.355	−	395.113i	−0.894582	−	0.516487i
$766$	982.989	+	295.395i	1.28328	+	0.385634i
$767$	219.312	−	126.620i	0.285935	−	0.165085i
$768$	−925.691	+	965.056i	−1.20533	+	1.25658i
$769$	−140.749			−0.183028			−0.0915142	−	0.995804i	$-0.529171\pi$
$769$	−140.749			−0.183028			−0.0915142	+	0.995804i	$0.529171\pi$
$770$		0			0
$771$	1265.99			1.64202
$772$	−739.527	−	488.588i	−0.957936	−	0.632886i
$773$	−1147.60	+	662.568i	−1.48461	+	0.857138i	−0.999847	−	0.0175096i	$-0.994426\pi$
$773$	−1147.60	+	662.568i	−1.48461	+	0.857138i	−0.484760	+	0.874647i	$0.661093\pi$
$774$	−371.950	+	1237.74i	−0.480555	+	1.59915i
$775$	88.6891	+	51.2047i	0.114437	+	0.0660705i
$776$	76.7200	−	63.9712i	0.0988660	−	0.0824371i
$777$		0			0
$778$	−1033.00	+	972.570i	−1.32777	+	1.25009i
$779$	−88.2183	+	152.799i	−0.113246	+	0.196147i
$780$	−283.109	+	141.450i	−0.362960	+	0.181347i
$781$	196.438	−	113.414i	0.251522	−	0.145216i
$782$	135.614	+	574.850i	0.173420	+	0.735102i
$783$		−	1811.81i		−	2.31393i
$784$		0			0
$785$	1179.50			1.50255
$786$	−542.278	+	127.930i	−0.689921	+	0.162761i
$787$	−163.900	−	283.884i	−0.208260	−	0.360716i	0.742907	−	0.669395i	$-0.233447\pi$
$787$	−163.900	−	283.884i	−0.208260	−	0.360716i	−0.951166	+	0.308679i	$0.900113\pi$
$788$	−433.181	−	867.000i	−0.549722	−	1.10025i
$789$	153.117	+	88.4021i	0.194065	+	0.112043i
$790$	171.285	+	181.929i	0.216817	+	0.230289i
$791$		0			0
$792$	−1101.86	+	918.764i	−1.39124	+	1.16006i
$793$	52.8819	−	91.5941i	0.0666859	−	0.115503i
$794$	−592.627	−	178.089i	−0.746382	−	0.224293i
$795$	894.898	+	1550.01i	1.12566	+	1.94970i
$796$	654.971	−	991.364i	0.822828	−	1.24543i
$797$			393.650i			0.493915i	0.969026	+	0.246958i	$0.0794308\pi$
$797$			393.650i			0.493915i	−0.969026	+	0.246958i	$0.920569\pi$
$798$		0			0
$799$		−	261.391i		−	0.327148i
$800$	−454.339	+	50.7250i	−0.567924	+	0.0634062i
$801$	−164.475	−	284.879i	−0.205337	−	0.355655i
$802$	−303.952	+	1011.46i	−0.378992	+	1.26117i
$803$	−339.453	+	587.950i	−0.422731	+	0.732192i
$804$	−39.1278	+	648.684i	−0.0486664	+	0.806821i
$805$		0			0
$806$	23.7488	+	25.2245i	0.0294650	+	0.0312959i
$807$	−749.132	−	432.511i	−0.928292	−	0.535950i
$808$	−187.852	+	511.178i	−0.232490	+	0.632646i
$809$	−208.321	−	360.822i	−0.257504	−	0.446010i	0.708069	−	0.706144i	$-0.249567\pi$
$809$	−208.321	−	360.822i	−0.257504	−	0.446010i	−0.965573	+	0.260134i	$0.916233\pi$
$810$	255.632	+	1083.59i	0.315595	+	1.33776i
$811$	748.707			0.923190			0.461595	−	0.887091i	$-0.347277\pi$
$811$	748.707			0.923190			0.461595	+	0.887091i	$0.347277\pi$
$812$		0			0
$813$			774.708i			0.952901i
$814$	0.912647	+	3.86858i	0.00112119	+	0.00475256i
$815$	−295.917	+	170.848i	−0.363089	+	0.209629i
$816$	−226.043	−	530.044i	−0.277014	−	0.649564i
$817$	−49.0562	+	84.9678i	−0.0600443	+	0.104000i
$818$	840.176	+	892.382i	1.02711	+	1.09093i
$819$		0			0
$820$	−1590.39	−	95.9302i	−1.93950	−	0.116988i
$821$	479.925	+	277.085i	0.584561	+	0.337496i	0.762944	−	0.646465i	$-0.223753\pi$
$821$	479.925	+	277.085i	0.584561	+	0.337496i	−0.178383	+	0.983961i	$0.557087\pi$
$822$	−173.538	+	577.483i	−0.211117	+	0.702534i
$823$	−105.180	+	60.7260i	−0.127801	+	0.0737861i	−0.562538	−	0.826772i	$-0.690175\pi$
$823$	−105.180	+	60.7260i	−0.127801	+	0.0737861i	0.434736	+	0.900558i	$0.356842\pi$
$824$	459.509	−	79.5549i	0.557656	−	0.0965472i
$825$	−731.853			−0.887094
$826$		0			0
$827$	−1516.61			−1.83386			−0.916932	−	0.399043i	$-0.869343\pi$
$827$	−1516.61			−1.83386			−0.916932	+	0.399043i	$0.869343\pi$
$828$	1727.05	−	2614.06i	2.08581	−	3.15707i
$829$	−281.494	+	162.521i	−0.339559	+	0.196044i	−0.660077	−	0.751198i	$-0.729476\pi$
$829$	−281.494	+	162.521i	−0.339559	+	0.196044i	0.320518	+	0.947242i	$0.396143\pi$
$830$	−61.4217	−	18.4577i	−0.0740021	−	0.0222382i
$831$	−2164.00	−	1249.38i	−2.60409	−	1.50347i
$832$	−152.139	−	27.8005i	−0.182859	−	0.0334140i
$833$		0			0
$834$	1234.80	+	1311.53i	1.48057	+	1.57257i
$835$	834.991	−	1446.25i	0.999989	−	1.73203i
$836$	−97.4265	+	48.6774i	−0.116539	+	0.0582265i
$837$	301.138	−	173.862i	0.359783	−	0.207721i
$838$	−462.586	+	109.130i	−0.552012	+	0.130227i
$839$		−	1165.70i		−	1.38939i	−0.719303	−	0.694696i	$-0.755539\pi$
$839$		−	1165.70i		−	1.38939i	0.719303	−	0.694696i	$-0.244461\pi$
$840$		0			0
$841$	−554.058			−0.658808
$842$	181.169	+	767.950i	0.215165	+	0.912055i
$843$	590.443	+	1022.68i	0.700407	+	1.21314i
$844$	−504.603	+	252.116i	−0.597870	+	0.298715i
$845$	885.658	+	511.335i	1.04812	+	0.605130i
$846$	−1009.54	+	950.482i	−1.19331	+	1.12350i
$847$		0			0
$848$	−105.132	+	868.301i	−0.123976	+	1.02394i
$849$	−665.041	+	1151.88i	−0.783323	+	1.35675i
$850$	56.6938	−	188.660i	0.0666986	−	0.221953i
$851$	−4.34013	−	7.51733i	−0.00510004	−	0.00883352i
$852$	266.400	−	403.223i	0.312676	−	0.473266i
$853$		−	151.949i		−	0.178134i	−0.996026	−	0.0890672i	$-0.971611\pi$
$853$		−	151.949i		−	0.178134i	0.996026	−	0.0890672i	$-0.0283886\pi$
$854$		0			0
$855$			318.218i			0.372184i
$856$	−185.424	−	1071.01i	−0.216617	−	1.25118i
$857$	206.009	+	356.818i	0.240384	+	0.416357i	0.960824	−	0.277160i	$-0.0893934\pi$
$857$	206.009	+	356.818i	0.240384	+	0.416357i	−0.720440	+	0.693517i	$0.756060\pi$
$858$	−237.111	−	71.2535i	−0.276353	−	0.0830461i
$859$	79.9965	−	138.558i	0.0931274	−	0.161301i	−0.815698	−	0.578478i	$-0.803647\pi$
$859$	79.9965	−	138.558i	0.0931274	−	0.161301i	0.908826	+	0.417176i	$0.136980\pi$
$860$	−884.380	−	53.3446i	−1.02835	−	0.0620286i
$861$		0			0
$862$	529.110	−	498.157i	0.613817	−	0.577908i
$863$	859.885	+	496.455i	0.996391	+	0.575266i	0.907178	−	0.420746i	$-0.138232\pi$
$863$	859.885	+	496.455i	0.996391	+	0.575266i	0.0892122	+	0.996013i	$0.471565\pi$
$864$	−622.182	+	1422.12i	−0.720118	+	1.64597i
$865$	359.886	+	623.341i	0.416053	+	0.720625i
$866$	233.069	−	54.9839i	0.269133	−	0.0634918i
$867$	−1261.33			−1.45482
$868$		0			0
$869$			195.479i			0.224947i
$870$	2380.45	−	561.577i	2.73614	−	0.645491i
$871$	−65.0896	+	37.5795i	−0.0747298	+	0.0431453i
$872$	−122.791	+	334.137i	−0.140815	+	0.383184i
$873$	114.165	−	197.740i	0.130773	−	0.226506i
$874$	173.169	−	163.038i	0.198133	−	0.186542i
$875$		0			0
$876$	−87.0912	+	1443.85i	−0.0994192	+	1.64823i
$877$	−714.554	−	412.548i	−0.814771	−	0.470408i	0.0338388	−	0.999427i	$-0.489227\pi$
$877$	−714.554	−	412.548i	−0.814771	−	0.470408i	−0.848610	+	0.529019i	$0.822560\pi$
$878$	−1669.21	−	501.611i	−1.90115	−	0.571311i
$879$	−676.570	+	390.618i	−0.769704	+	0.444389i
$880$	−786.447	−	590.560i	−0.893690	−	0.671090i
$881$	−1352.83			−1.53556			−0.767780	−	0.640714i	$-0.778639\pi$
$881$	−1352.83			−1.53556			−0.767780	+	0.640714i	$0.778639\pi$
$882$		0			0
$883$	−1013.40			−1.14768			−0.573838	−	0.818969i	$-0.694546\pi$
$883$	−1013.40			−1.14768			−0.573838	+	0.818969i	$0.694546\pi$
$884$	36.7361	−	55.6038i	0.0415567	−	0.0629002i
$885$	2971.42	−	1715.55i	3.35754	−	1.93847i
$886$	−197.977	+	658.808i	−0.223450	+	0.743575i
$887$	202.442	+	116.880i	0.228233	+	0.131770i	0.609756	−	0.792589i	$-0.291267\pi$
$887$	202.442	+	116.880i	0.228233	+	0.131770i	−0.381524	+	0.924359i	$0.624601\pi$
$888$	5.42340	+	6.50422i	0.00610743	+	0.00732457i
$889$		0			0
$890$	164.186	−	154.581i	0.184478	−	0.173686i
$891$	−435.487	+	754.285i	−0.488762	+	0.846561i
$892$	72.9899	+	146.087i	0.0818273	+	0.163775i
$893$	−91.1580	+	52.6301i	−0.102081	+	0.0589363i
$894$	−526.603	−	2232.20i	−0.589042	−	2.49686i
$895$		−	707.322i		−	0.790304i
$896$		0			0
$897$	540.686			0.602772
$898$	472.721	−	111.521i	0.526416	−	0.124188i
$899$	−133.871	−	231.871i	−0.148911	−	0.257921i
$900$	−934.793	+	467.052i	−1.03866	+	0.518947i
$901$	−326.396	−	188.445i	−0.362260	−	0.209151i
$902$	−854.423	−	907.514i	−0.947254	−	1.00611i
$903$		0			0
$904$	819.589	−	683.396i	0.906625	−	0.755968i
$905$	191.004	−	330.829i	0.211054	−	0.365557i
$906$	−1857.66	−	558.240i	−2.05039	−	0.616159i
$907$	101.795	+	176.314i	0.112233	+	0.194393i	0.916670	−	0.399645i	$-0.130866\pi$
$907$	101.795	+	176.314i	0.112233	+	0.194393i	−0.804438	+	0.594037i	$0.797533\pi$
$908$	27.3199	+	18.0496i	0.0300880	+	0.0198784i
$909$			1244.85i			1.36947i
$910$		0			0
$911$		−	712.022i		−	0.781583i	−0.920479	−	0.390792i	$-0.872201\pi$
$911$		−	712.022i		−	0.781583i	0.920479	−	0.390792i	$-0.127799\pi$
$912$	−139.336	+	185.553i	−0.152780	+	0.203457i
$913$	−25.0869	−	43.4517i	−0.0274774	−	0.0475922i
$914$	−24.3226	+	80.9385i	−0.0266112	+	0.0885542i
$915$	716.487	−	1240.99i	0.783046	−	1.35628i
$916$	−1326.60	−	80.0185i	−1.44825	−	0.0873564i
$917$		0			0
$918$	−458.512	−	487.002i	−0.499468	−	0.530503i
$919$	−681.374	−	393.391i	−0.741430	−	0.428065i	0.0811591	−	0.996701i	$-0.474138\pi$
$919$	−681.374	−	393.391i	−0.741430	−	0.428065i	−0.822589	+	0.568636i	$0.807471\pi$
$920$	2015.97	+	740.844i	2.19127	+	0.805266i
$921$	709.836	+	1229.47i	0.770723	+	1.33493i
$922$	374.893	+	1589.12i	0.406608	+	1.72355i
$923$	55.8929			0.0605557
$924$		0			0
$925$			2.89516i			0.00312990i
$926$	−52.8839	−	224.168i	−0.0571101	−	0.242082i
$927$	923.154	−	532.983i	0.995851	−	0.574955i
$928$	1095.00	+	479.068i	1.17996	+	0.516237i
$929$	−828.996	+	1435.86i	−0.892353	+	1.54560i	−0.0553061	+	0.998469i	$0.517613\pi$
$929$	−828.996	+	1435.86i	−0.892353	+	1.54560i	−0.837047	+	0.547131i	$0.815720\pi$
$930$	321.768	+	341.761i	0.345987	+	0.367485i
$931$		0			0
$932$	−79.2981	+	1314.65i	−0.0850838	+	1.41057i
$933$	2416.52	+	1395.18i	2.59006	+	1.49537i
$934$	−347.323	+	1155.79i	−0.371866	+	1.23746i
$935$	367.017	−	211.897i	0.392532	−	0.226628i
$936$	−348.333	+	60.3070i	−0.372151	+	0.0644306i
$937$	−333.736			−0.356175			−0.178088	−	0.984015i	$-0.556991\pi$
$937$	−333.736			−0.356175			−0.178088	+	0.984015i	$0.556991\pi$
$938$		0			0
$939$	2905.55			3.09430
$940$	−793.078	−	523.968i	−0.843700	−	0.557413i
$941$	470.533	−	271.662i	0.500035	−	0.288695i	−0.228693	−	0.973499i	$-0.573445\pi$
$941$	470.533	−	271.662i	0.500035	−	0.288695i	0.728728	+	0.684803i	$0.240112\pi$
$942$	1882.81	+	565.798i	1.99874	+	0.600635i
$943$	2357.34	+	1361.01i	2.49984	+	1.44328i
$944$	1664.56	+	201.542i	1.76331	+	0.213497i
$945$		0			0
$946$	−475.125	−	504.648i	−0.502247	−	0.533454i
$947$	179.864	−	311.534i	0.189930	−	0.328969i	−0.755296	−	0.655383i	$-0.772507\pi$
$947$	179.864	−	311.534i	0.189930	−	0.328969i	0.945227	+	0.326414i	$0.105840\pi$
$948$	186.149	+	372.572i	0.196360	+	0.393009i
$949$	−144.878	+	83.6451i	−0.152663	+	0.0881403i
$950$	−77.2088	+	18.2145i	−0.0812724	+	0.0191732i
$951$		−	2023.94i		−	2.12823i
$952$		0			0
$953$	−904.225			−0.948820			−0.474410	−	0.880304i	$-0.657339\pi$
$953$	−904.225			−0.948820			−0.474410	+	0.880304i	$0.657339\pi$
$954$	459.046	+	1945.83i	0.481181	+	2.03966i
$955$	559.281	+	968.702i	0.585634	+	1.01435i
$956$	246.214	+	492.791i	0.257546	+	0.515472i
$957$	1657.03	+	956.686i	1.73148	+	0.999672i
$958$	230.941	−	217.431i	0.241066	−	0.226963i
$959$		0			0
$960$	−2061.30	−	376.663i	−2.14719	−	0.392358i
$961$	−454.807	+	787.749i	−0.473265	+	0.819719i
$962$	−0.281874	+	0.937994i	−0.000293008	+	0.000975045i
$963$	−1242.26	−	2151.66i	−1.28999	−	2.23433i
$964$	673.666	+	445.075i	0.698823	+	0.461697i
$965$		−	1388.89i		−	1.43926i
$966$		0			0
$967$			920.961i			0.952390i	0.879340	+	0.476195i	$0.157984\pi$
$967$			920.961i			0.952390i	−0.879340	+	0.476195i	$0.842016\pi$
$968$	33.8798	+	195.689i	0.0349997	+	0.202159i
$969$	−49.9947	−	86.5933i	−0.0515941	−	0.0893636i
$970$	149.904	+	45.0474i	0.154541	+	0.0464406i
$971$	663.655	−	1149.48i	0.683476	−	1.18381i	−0.290438	−	0.956894i	$-0.593801\pi$
$971$	663.655	−	1149.48i	0.683476	−	1.18381i	0.973913	−	0.226921i	$-0.0728658\pi$
$972$	−6.58670	+	109.198i	−0.00677644	+	0.112344i
$973$		0			0
$974$	155.791	−	146.677i	0.159950	−	0.150593i
$975$	−156.176	−	90.1684i	−0.160181	−	0.0924805i
$976$	644.140	−	274.701i	0.659980	−	0.281456i
$977$	344.245	+	596.250i	0.352349	+	0.610286i	0.986661	−	0.162791i	$-0.0520497\pi$
$977$	344.245	+	596.250i	0.352349	+	0.610286i	−0.634312	+	0.773077i	$0.718716\pi$
$978$	−554.320	+	130.771i	−0.566789	+	0.133713i
$979$	176.415			0.180199
$980$		0			0
$981$			813.706i			0.829466i
$982$	−1200.24	+	283.151i	−1.22224	+	0.288341i
$983$	1461.05	−	843.539i	1.48632	−	0.858127i	0.486441	−	0.873714i	$-0.338295\pi$
$983$	1461.05	−	843.539i	1.48632	−	0.858127i	0.999879	+	0.0155866i	$0.00496158\pi$
$984$	−2492.68	−	916.029i	−2.53321	−	0.930924i
$985$	759.348	−	1315.23i	0.770912	−	1.33526i
$986$	−374.983	+	353.046i	−0.380307	+	0.358058i
$987$		0			0
$988$	−26.7880	−	1.61582i	−0.0271134	−	0.00163544i
$989$	1310.87	+	756.829i	1.32545	+	0.765246i
$990$	−2152.95	−	646.977i	−2.17470	−	0.653512i
$991$	−986.597	+	569.612i	−0.995557	+	0.574785i	−0.906931	−	0.421280i	$-0.861581\pi$
$991$	−986.597	+	569.612i	−0.995557	+	0.574785i	−0.0886266	+	0.996065i	$0.528248\pi$
$992$	25.4519	+	227.971i	0.0256572	+	0.229809i
$993$	−2001.72			−2.01583
$994$		0			0
$995$	1861.85			1.87121
$996$	−89.1920	−	58.9271i	−0.0895502	−	0.0591637i
$997$	−178.475	+	103.043i	−0.179012	+	0.103353i	−0.586828	−	0.809711i	$-0.699624\pi$
$997$	−178.475	+	103.043i	−0.179012	+	0.103353i	0.407816	+	0.913064i	$0.366290\pi$
$998$	318.927	−	1061.30i	0.319566	−	1.06342i
$999$	8.51331	+	4.91516i	0.00852183	+	0.00492008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.n.275.1		16
7.2	even	3		392.3.g.m.99.6		8
7.3	odd	6		392.3.k.o.67.6		16
7.4	even	3	inner	392.3.k.n.67.6		16
7.5	odd	6		56.3.g.b.43.6	yes	8
7.6	odd	2		392.3.k.o.275.1		16
8.3	odd	2	inner	392.3.k.n.275.6		16
21.5	even	6		504.3.g.b.379.3		8
28.19	even	6		224.3.g.b.15.8		8
28.23	odd	6		1568.3.g.m.687.1		8
56.3	even	6		392.3.k.o.67.1		16
56.5	odd	6		224.3.g.b.15.7		8
56.11	odd	6	inner	392.3.k.n.67.1		16
56.19	even	6		56.3.g.b.43.5	✓	8
56.27	even	2		392.3.k.o.275.6		16
56.37	even	6		1568.3.g.m.687.2		8
56.51	odd	6		392.3.g.m.99.5		8
84.47	odd	6		2016.3.g.b.1135.1		8
112.5	odd	12		1792.3.d.j.1023.15		16
112.19	even	12		1792.3.d.j.1023.16		16
112.61	odd	12		1792.3.d.j.1023.2		16
112.75	even	12		1792.3.d.j.1023.1		16
168.5	even	6		2016.3.g.b.1135.8		8
168.131	odd	6		504.3.g.b.379.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.5	✓	8	56.19	even	6
56.3.g.b.43.6	yes	8	7.5	odd	6
224.3.g.b.15.7		8	56.5	odd	6
224.3.g.b.15.8		8	28.19	even	6
392.3.g.m.99.5		8	56.51	odd	6
392.3.g.m.99.6		8	7.2	even	3
392.3.k.n.67.1		16	56.11	odd	6	inner
392.3.k.n.67.6		16	7.4	even	3	inner
392.3.k.n.275.1		16	1.1	even	1	trivial
392.3.k.n.275.6		16	8.3	odd	2	inner
392.3.k.o.67.1		16	56.3	even	6
392.3.k.o.67.6		16	7.3	odd	6
392.3.k.o.275.1		16	7.6	odd	2
392.3.k.o.275.6		16	56.27	even	2
504.3.g.b.379.3		8	21.5	even	6
504.3.g.b.379.4		8	168.131	odd	6
1568.3.g.m.687.1		8	28.23	odd	6
1568.3.g.m.687.2		8	56.37	even	6
1792.3.d.j.1023.1		16	112.75	even	12
1792.3.d.j.1023.2		16	112.61	odd	12
1792.3.d.j.1023.15		16	112.5	odd	12
1792.3.d.j.1023.16		16	112.19	even	12
2016.3.g.b.1135.1		8	84.47	odd	6
2016.3.g.b.1135.8		8	168.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.94657 + 0.459219i) q^{2} +(-2.61182 - 4.52380i) q^{3} +(3.57824 - 1.78780i) q^{4} +(5.42814 + 3.13394i) q^{5} +(7.16148 + 7.60647i) q^{6} +(-6.14428 + 5.12327i) q^{8} +(-9.14316 + 15.8364i) q^{9} +O(q^{10})\)	\(q+(-1.94657 + 0.459219i) q^{2} +(-2.61182 - 4.52380i) q^{3} +(3.57824 - 1.78780i) q^{4} +(5.42814 + 3.13394i) q^{5} +(7.16148 + 7.60647i) q^{6} +(-6.14428 + 5.12327i) q^{8} +(-9.14316 + 15.8364i) q^{9} +(-12.0054 - 3.60771i) q^{10} +(-4.90344 - 8.49301i) q^{11} +(-17.4333 - 11.5178i) q^{12} -2.41653i q^{13} -32.7411i q^{15} +(9.60754 - 12.7943i) q^{16} +(3.44726 + 5.97083i) q^{17} +(10.5254 - 35.0253i) q^{18} +(1.38818 - 2.40441i) q^{19} +(25.0260 + 1.50954i) q^{20} +(13.4450 + 14.2804i) q^{22} +(-37.0947 - 21.4166i) q^{23} +(39.2243 + 14.4144i) q^{24} +(7.14316 + 12.3723i) q^{25} +(1.10972 + 4.70393i) q^{26} +48.5083 q^{27} -37.3505i q^{29} +(15.0353 + 63.7327i) q^{30} +(6.20797 - 3.58417i) q^{31} +(-12.8263 + 29.3170i) q^{32} +(-25.6138 + 44.3643i) q^{33} +(-9.45224 - 10.0396i) q^{34} +(-4.40402 + 73.0126i) q^{36} +(0.175502 + 0.101326i) q^{37} +(-1.59804 + 5.31782i) q^{38} +(-10.9319 + 6.31153i) q^{39} +(-49.4080 + 8.55402i) q^{40} -63.5494 q^{41} -35.3384 q^{43} +(-32.7295 - 21.6236i) q^{44} +(-99.2607 + 57.3082i) q^{45} +(82.0421 + 24.6543i) q^{46} +(-32.8335 - 18.9564i) q^{47} +(-82.9721 - 10.0461i) q^{48} +(-19.5862 - 20.8032i) q^{50} +(18.0072 - 31.1894i) q^{51} +(-4.32027 - 8.64691i) q^{52} +(-47.3414 + 27.3326i) q^{53} +(-94.4246 + 22.2759i) q^{54} -61.4684i q^{55} -14.5027 q^{57} +(17.1521 + 72.7051i) q^{58} +(52.3975 + 90.7551i) q^{59} +(-58.5345 - 117.155i) q^{60} +(37.9032 + 21.8834i) q^{61} +(-10.4383 + 9.82765i) q^{62} +(11.5043 - 62.9575i) q^{64} +(7.57325 - 13.1173i) q^{65} +(29.4859 - 98.1204i) q^{66} +(-15.5510 - 26.9352i) q^{67} +(23.0098 + 15.2020i) q^{68} +223.745i q^{69} +23.1294i q^{71} +(-24.9561 - 144.146i) q^{72} +(-34.6138 - 59.9528i) q^{73} +(-0.388158 - 0.116644i) q^{74} +(37.3132 - 64.6284i) q^{75} +(0.668652 - 11.0853i) q^{76} +(18.3813 - 17.3059i) q^{78} +(-17.2624 - 9.96642i) q^{79} +(92.2478 - 39.3401i) q^{80} +(-44.4063 - 76.9139i) q^{81} +(123.703 - 29.1831i) q^{82} +5.11617 q^{83} +43.2140i q^{85} +(68.7885 - 16.2281i) q^{86} +(-168.966 + 97.5525i) q^{87} +(73.6400 + 27.0618i) q^{88} +(-8.99444 + 15.5788i) q^{89} +(166.901 - 157.137i) q^{90} +(-171.022 - 10.3158i) q^{92} +(-32.4282 - 18.7224i) q^{93} +(72.6178 + 21.8222i) q^{94} +(15.0705 - 8.70097i) q^{95} +(166.124 - 18.5470i) q^{96} -12.4864 q^{97} +179.332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Introduction

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